The 13th-seeded Navarro took advantage of third-ranked Gauff's 19 double faults and 60 unforced errors to win 6-3, 4-6, 6-3 and set up a quarter-final against Spain's Paula Badosa.
Gauff's defeat means that Serena Williams remains the last woman to successfully defend the US Open title back in 2014.
Navarro had defeated Gauff at Wimbledon in July and was dominant again on Sunday from the outset.
The New Yorker broke for 4-2 in the first set and sealed the opener in the ninth game where one rally stretched to 27 shots.
Gauff was undone by 21 unforced errors to Navarro's meagre eight.
Navarro stretched to a 4-3 lead in the second set with another break after Gauff had committed her eighth double fault of the tie.
However, Gauff, who had dropped the first set in her third-round win against Elina Svitolina, hit back to reel off the next three games and level the match.
It was just a brief respite for the 20-year-old as she served up three more double faults in the third game of the decider to slip a breakdown again.
There was no coming back for the champion as Navarro moved into the last eight in her home city tournament for the first time.
